[1][2] Due to the rise of fellow Australian Murray Rose in distance freestyle swimming, Chapman switched to competing in the 110 yd and 220-yard freestyle events in a bid to increase his chances of success at the 1956 Olympics in Melbourne.

Prior to the games, he defeated teammate Jon Henricks twice in the 220-yard freestyle, setting a world record on one of those occasions.

He won the bronze medal in 100-metre freestyle, finishing behind Henricks and another Australian, John Devitt.

As the 220-yard freestyle world record, Chapman was snubbed by the selectors in the 4×200-metre freestyle relay, only swimming in the qualifying heats, but being replaced by Kevin O'Halloran in the final, where the Australians won the gold medal in a world record time.

Under the rules of the time, heat swimmers were not entitled to gold medals.